JEE MainPhysicsCapacitance
A capacitor is constructed with a flat bottom plate of area A and a stepped top plate. The stepped plate has three horizontal sections, each of area A 3 . The separations between the bottom plate and the three sections are d , 2d , and 3d respectively. The gap of the first section (with separation d ) is completely filled with a dielectric material of dielectric constant K = 2 . The other two gaps are filled with air
Options
- A11 ₀ A 18 d
- B11 ₀ A 9 d
- C2 ₀ A 33 d
- D17 ₀ A 18 d
Correct answer
D. 17 ₀ A 18 d
Step-by-step solution
The arrangement can be modeled as three capacitors connected in parallel, each having an area of A 3 . The first capacitor has a plate separation d and is filled with a dielectric of K = 2 . Its capacitance is: C₁ = K ₀ ( A 3 ) d = 2 ₀ A 3d The second capacitor has a plate separation 2d and is filled with air. Its capacitance is: C₂ = ₀ ( A 3 ) 2d = ₀ A 6d The third capacitor has a plate separation 3d and is filled with air. Its capacitance is: C₃ = ₀ ( A 3 ) 3d = ₀ A 9d Since they are in parallel, the equivalent c